The present invention relates generally to apparatuses and methods for measuring a shape of a surface, and more particularly to an interferometer and an interference measurement method. The present invention is used suitably to measure, with high accuracy, a wide range of surface shapes from a spherical surface to an aspheric surface of a target object.
The present invention is also used suitably to measure, with high precision, surface shapes including a spherical surface, an aspheric surface, etc., of each optical element (e.g., a lens, a filter, etc.) in a projection optical system for use with a lithography process that transfers a pattern on a mask onto a photosensitive substrate, and manufactures a semiconductor device, etc.
Innovations in optical systems have always been promoted by introductions of a new optical element and/or a degree of freedom. Among them, recent developments in process and measurement methods have successfully applied optical performance improved by the advent of aspheric surfaces, which has been sought in astronomical telescopes, to semiconductor exposure apparatuses used to manufacture semiconductor devices, which require extremely high accuracy.
There are three major advantages in a semiconductor exposure apparatus using an aspheric surface: The first advantage is the reduced number of optical elements. An optical system in a semiconductor exposure apparatus has necessarily required such expensive materials, as quartz and fluorite, as it requires a shorter wavelength. The reduced number of optical elements as an advantage of the aspheric surface is remarkably preferable for manufacture and cost-reduction purposes. The second advantage is miniaturization. The size reduction as another advantage of the aspheric surface still has drastically promoted manufacture and cost reduction. The third advantage is high performance. Aspheric surfaces are expected to play a more important role to realize an optical system that has increasingly required the high-accuracy performance as a high numerical aperture (“NA”) and low aberration advance.
A system using Extreme Ultra Violet (“EUV”) light is the likeliest to be elected for an exposure method of next generation in view of recent accelerating demands for more minute patterns. The EUV system uses light having such a short wavelength as 13.4 nm, which is below one-tenth of a wavelength of light that has been used for conventional exposure, and a reflective image-forming optical system to transfer an image on a reticle onto a wafer. Wavelengths in the EUV range are too short for optical members (or transmissive materials) to transmit the EUV light, and the optical system uses only mirrors with no lenses. In addition, the EUV range restricts usable reflective materials, and mirror's reflectance for each surface becomes a little less than 70%. Therefore, such a structure as seen in conventional optical systems that use twenty or more lenses is not applicable in view of optical use efficiency. It is necessary to use optical elements as few as possible to form an image-forming optical system that meets desired performance.
Current EUV prototype machines use a three- or four-mirror system with an NA of about 0.10, but prospective systems are expected to use a six-mirror system with an NA of 0.25 to 0.30. As one solution for breaking down such a conventional wall and for realizing a high-performance optical system with fewer elements, it is the necessary technology to actually precisely process and measure aspheric surfaces so as to obtain an optical element with a predetermined surface shape.
However, even when a designed value provides high performance, a conventional aspheric-surface process disadvantageously has the limited measurement accuracy of the aspheric surface and cannot process a surface exceeding a predetermined aspheric surface amount, which is determined by a measurable range with desired precision. As is well known, the measurement and process are interrelated with each other; no precise process is available without good measurement accuracy.
The spherical-shape measurement is the most commonly used technology to measure optical elements, and there are many general-purpose apparatuses with advanced precision due to continuous endeavors toward precision improvement. However, it is difficult for the aspheric surface amount ten times as large as a measuring wavelength to keep the same measurement precision as the spherical measurement since an interval in an interference fringe is excessively small.
Usually, the Computer Generated Hologram (“CGH”) and means for generating a wave front of a desired aspheric surface using a dedicated null lens have been well known as approaches to measure large aspheric surfaces. However, these conventional approaches have been found to be unavailable for an optical system for semiconductor exposure apparatuses, regardless of whether they have other applications, because manufacture precisions for the CGH or null lens are insufficient for the semiconductor exposure apparatuses, and the CGH uses diffracted light and arduously requires 0-order light process.
There has been known another approach for measuring aspheric surfaces using a mechanical or optical probe. Although a probe is so flexible that it is compatible with various shaped aspheric surfaces, the probe disadvantageously has measurement limits and exhibits instability during a positional measurement. Therefore, this approach hardly provides so precise as an interference measurement method.
One known method of measuring an aspheric shape uses a normal spherical-shape measuring interferometer to measure only a segment (which has usually a strap shape) where curvature radii on a spherical surface and an aspheric surface accord with each other, and then measures an entire surface by gradually changing a curvature radius to be measured. However, this method includes the following disadvantages:
A target optical system is often co-axial, and thus its optical element often has a rotational symmetry. In general, an aspheric shape is described only by terms of even orders as in an equation (1) below where r is a distance from an optical axis (or a radius or a moving radius), c is a curvature of paraxial spherical surface at the radius r in the optical-axis direction, and z is the optical-axis direction:                     z        =                                                            cr                2                                            1                +                                                      1                    -                                                                  (                                                  1                          +                          k                                                )                                            ⁢                                              c                        2                                            ⁢                                              r                        2                                                                                                                  +                          Ar              2                        +                          Br              6                        +                          Cr              8                        +                          Dr              10                        +                          Er              12                        +                          Fr              14                        +                          Gr              16                                ≈                                                    1                2                            ⁢                                                           ⁢                              cr                2                                      +                                          {                                                                            1                      8                                        ⁢                                                                  c                        3                                            ⁡                                              (                                                  1                          +                          K                                                )                                                                              +                  A                                }                            ⁢                              r                4                                      +                                          {                                                                            1                      16                                        ⁢                                                                                            c                          5                                                ⁡                                                  (                                                      1                            +                            K                                                    )                                                                    2                                                        +                  B                                }                            ⁢                              r                6                                      +                                          {                                                                            5                      128                                        ⁢                                                                                            c                          7                                                ⁡                                                  (                                                      1                            +                            K                                                    )                                                                    3                                                        +                  C                                }                            ⁢                              r                8                                      +                                          {                                                                            7                      256                                        ⁢                                                                                            c                          9                                                ⁡                                                  (                                                      1                            +                            K                                                    )                                                                    4                                                        +                  D                                }                            ⁢                              r                10                                                                        (        1        )            
Where K=A=B=C=D=0 in the equation (1), z becomes a spherical surface with a curvature radius R=1/c. Thus, an offset amount (or aspheric amount) 5 from the spherical surface is defined as a subtraction of the spherical surface from the equation (1), which is expanded and expressed only by terms of fourth or higher orders of the distance r as in the following equation (2):                     δ        =                                            {                                                                    1                    8                                    ⁢                                      c                    3                                    ⁢                  K                                +                A                            }                        ⁢                          r              4                                +                                    {                                                                    1                    16                                    ⁢                                      c                    5                                    ⁢                                      K                    ⁡                                          (                                              2                        +                        K                                            )                                                                      +                B                            }                        ⁢                          r              6                                +                                    {                                                                    5                    128                                    ⁢                                      c                    7                                    ⁢                                      K                    ⁡                                          (                                              3                        +                                                  3                          ⁢                                                                                                           ⁢                          K                                                +                                                  K                          2                                                                    )                                                                      +                C                            }                        ⁢                          r              8                                +                                    {                                                                    7                    256                                    ⁢                                      c                    9                                    ⁢                                      K                    ⁡                                          (                                              4                        +                                                  6                          ⁢                                                                                                           ⁢                          K                                                +                                                  4                          ⁢                                                                                                           ⁢                                                      K                            2                                                                          +                                                  K                          3                                                                    )                                                                      +                D                            }                        ⁢                          r              10                                                          (        2        )            
The term of the fourth order of the distance r is particularly important for an aspheric amount. In this case, a usual reference side uses a plane mirror, and this offset amount δ corresponds to an offset of a wave front at the time of producing an interference fringe. When the offset amount δ exceeds ten times wavelength of measuring light, the measurement becomes difficult due to a too short interval between interference fringes.